混合相依过程局部多项式加权回归估计渐近正态性的进一步结果

Further Result of the Asymptotic Normality of Weighted Local Polynomial Regression Estimation Under Dependent Process

对相依时间序列数据 ,在一定的条件下已有人证明了局部多项式加权回归系数估计服从渐近正态分布 ,其中核函数是有界的 .但在非线性相依过程 (如 ρ 混合过程和强混合过程 )中 ,当数据之间的相依程度较大时 ,这种核函数便失去其合理性 ,作者在更广泛的核函数空间上考虑了这个问题 。

Fan J and Gijbels I gave the asymptotic normality of local polynomial regression estimation in dependent time series,where the weighted function is bounded.The authors generize the result where weight function space is a more general space.This kind of weight function will be more sufficient in nonlinear dependent processes such as ρ mixing and strongly mixing processes.In this case,the model can be more reasonablly used in economic time series.